In the conventional procedure and machine for producing rubber gaskets, seals and the like, uncured rubber material is fed into an extruder wherein an auger propels the material to and through a die which forms a sleeve or tube of the desired length, usually two or three feet in length, before it is severed from the die. The rubber material is heated either before the material is introduced into the extruder and/or while it is in the extruder, to the temperature required to plasticize the material so that it will conform to the die and form the tubular extrusion. The extruded sleeve, which is normally quite flexible, is cooled and a first mandrel is inserted in the sleeve for curing and sizing of the sleeve. The sleeve is then removed from the first mandrel and a second mandrel is inserted in the sleeve and the external surface of the sleeve is ground to the desired external dimension, after which a third mandrel is inserted in the sleeve, and the mandrel and sleeve are inserted in a lathe where the rubber sleeve is cut into rings for gaskets, seals and the like by a knife or other tool moved radially inwardly while the mandrel and sleeve are rotating in the lathe. This conventional method of producing the rings requires three separate handling operations in which the three mandrels are inserted in each individual sleeve. These operations require a substantial amount of labor and time to complete the full procedure from the extruding step to the final step in which the severed rings are removed from the third mandrel.